Question 1
If is an even integer and is an odd integer, which of the following must be odd?
- A
- B
- C
- D
Show answer
Answer: D —
An even integer plus an odd integer is odd, so must be odd. Each other expression contains an even factor.
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Real number system and number properties — ACT practice questions
On the ACT Mathematics test, Real number system and number properties covers even and odd integers, shared multiples, and signed numbers on a number line. Students must reason about parity of sums and products, count values that are multiples of both given intervals, and find total distance after a sequence of moves rather than net displacement. Items are multiple choice. Typical traps include treating an even-odd product as odd, using a greatest common factor where a least common multiple is needed, and reporting the final position or the change from start to finish instead of the path length. Answer choices usually mix even and odd expressions or nearby integer distances.
- Section: Mathematics 45 questions on the paper
- 59 practice questions in the app
Sample questions
Question 2
A museum tour offered a free map to every 16th guest and a free pin to every 24th guest. Given that 960 guests entered during the day, how many guests received both a free map and a free pin?
- A10
- B20
- C30
- D40
Show answer
Answer: B — 20
. Then .
Question 3
A cart starts at -3 on a number line, moves to 8, and then moves to -6. What total distance does the cart travel?
- A3
- B11
- C14
- D25
Show answer
Answer: D — 25
The two distances are and . Therefore, the total distance is .
Practice 59 Real number system and number properties questions in the app
More ACT topics
Mathematics
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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